ROBUST FINITE ELEMENTS FOR 3D‐ANALYSIS OF RUBBER‐LIKE MATERIALS

Abstract

A marked characteristic of rubber-like materials is the nearly incompressible behaviour. This type of behaviour is best modelled by mixed finite elements with separate interpolation functions for the displacements and the pressure. In this contribution the performance of three-dimensional elements is investigated using a two-tiered strategy. First, the ability of some linear and quadratic three-dimensional elements to deform correctly under nearly isochoric conditions is estimated using the well-known constraint-counting method, in which the ratio of the number of degrees-of-freedom over the number of kinematic constraints present in the finite element mesh is determined. Next, the performance of the elements is assessed by numerical simulations for three cuboidal rubber blocks with different shape factors. The results turn out to be quite sensitive with respect to the ratio of the number of degrees-of-freedom over the number of kinematic constraints, since too many pressure degrees-of-freedom make the element overstiff, while too few pressure degrees-of-freedom may cause the occurrence of spurious kinematic modes. This observation appears to be not only valid for the global structural behaviour, but also with respect to the specific parts in the structure, where the above-mentioned ratio is different from the global number, e.g., in corners of the structure.